Philosophiae Doctor - PhD / This study attempts to understand how distance education practices influence the learning of calculus. Understanding student learning in a distance education environment is an important factor to consider in improving the learning experiences of those students who for one reason or the other opt not to study in conventional institutions of higher education. On one hand, understanding student learning may illuminate the influences that the learning environment has on student learning and on the other hand, it may inform on how learning experiences can be improved. The aim of this study is to acquire a deeper understanding of the diverse manner in which distance students learn calculus. Specific focus is also placed on how the distance education context of the Zimbabwe Open University (ZOU) influences student learning. The study describes a group of students' experiences of learning calculus in the ZOU distance education environment. The study also describes the students' learning styles and relates these to their mathematical understanding of certain calculus concepts. The specific content topics of "limit of function" and "derivative of function" are used to view achievement and performance, thereby indicating the distance students' mathematical understanding. The information processing learning theory is used as the theoretical framework for this study. The constructs of learning styles and mathematical understanding are used to illuminate the student's learning processes. The study used the Felder-Silverman learning styles model and Hiebert and Carpenter's notion of mathematical understanding to expound these constructs. The distance education environment of the B.Sc. Mathematics and Statistics (BSMS) programme at the ZOU provided the context of the study and an interpretive case study approach was adopted. A group of students registered in a first year first semester calculus course were studied. Data were collected from students based in four ZOU regional centres; namely Harare, Mashonaland Central, Mashonaland West, and Masvingo. These regional centres were conveniently selected for the study on the basis of proximity and accessibility. A total sample of twenty six students was involved and data for the in-depth part of the study emanated from five students who were purposively selected to participate in interviews. The interviewees were selected on the basis of their performance in a written calculus test. Data for this study were collected through use of learning journals, learning styles preference questionnaires, calculus tests and interviews. The data on students' learning experiences were predominantly qualitative in nature though supported by some quantitative data. The data on learning styles and mathematical understanding were also qualitatively analysed and presented case by case for the five interviewees. The study established that in a distance education system, the type of learning environment has the potential to influence students' learning, both positively and negatively, of which the main contributing factor is the learning support system. The study found that the learning support system provided by the institution and distance educators can have an impact on student learning. With reference to the calculus course in the BSMS programme, the study identified specific aspects where the environment facilitated or deterred learning. The study also revealed that students have varied learning style preferences, and that the learning environment has the potential to impact on students' learning styles. Since learning styles occupy a central place when it comes to improving distance learning materials, the study further explored the relationship between the constructs of learning styles and mathematical understanding. The study revealed that students' learning styles can influence the students' mathematical understanding. Improving students' learning in a distance education environment rests mainly on improving the learning materials and the support systems. A carefully designed and well supported instructional distance learning package can facilitate learning. Implications of the findings point towards the improvement of the distance teaching processes through the improvement of learning materials and the learning support systems for the BSMS distance education programme.

The purpose of the present study is to describe adult second language learners’ experiences of mathematics learning from a past and contemporary perspective. What experiences in mathematics do they bring? What does it mean to learn Mathematics through their new language? The study is based on life-world narratives from five second language students with another native language than Swedish. Today they all study at a Swedish folk high school, at upper secondary level and they have previously studied at this level in Mathematics.   The result shows that the meeting with the Swedish school and folk high school context is confusing. They face a new school culture with quite different normative rules and it is unclear to them how to behave as good students in this context. They are positive about the response from teachers which is much unlike their previously experiences. The teachers are competent tutors, supportive, listening, encouraging, friendly, authorities without being iron handed.   The multilingual students in this study describe that the new language is of secondary importance in mathematics learning. Everyone starts off  in year one at upper secondary level and sees mathematics the first period as a refresher. Mathematic studies are, during this period, used to consolidate the mathematical concepts in the new language. All change automatically to their native or previous school language when working with mathematical tasks. There are basic mathematical  concepts learned and automated, it is too cognitively demanding to use the Swedish language. They are critical of how Mathematics is taught, a lot of individual work and pace and says that briefings and discussions are more effective, a teacher led approach that they are familiar with.

This study investigates the possibilities and implications for the teaching of the solving of polynomial equations. It is historically directed and also focusses on the working procedures in algebra which target the cognitive and affective domains. The teaching implications of the development of representational styles of equations and their solving procedures are noted. Since concepts in algebra can be conceived as processes or objects this leads to cognitive obstacles, for example: a limited view of the equal sign, which result in learning and reasoning problems. The roles of sense-making, visual imagery, mental schemata and networks in promoting meaningful understanding are scrutinised. Questions and problems to solve are formulated to promote the processes associated with the solving of polynomial equations, and the solving procedures used by a group of college students are analysed. A teaching model/method, which targets the cognitive and affective domains, is presented. / Mathematics Education / M.A. (Mathematics Education)

This study investigates the possibilities and implications for the teaching of the solving of polynomial equations. It is historically directed and also focusses on the working procedures in algebra which target the cognitive and affective domains. The teaching implications of the development of representational styles of equations and their solving procedures are noted. Since concepts in algebra can be conceived as processes or objects this leads to cognitive obstacles, for example: a limited view of the equal sign, which result in learning and reasoning problems. The roles of sense-making, visual imagery, mental schemata and networks in promoting meaningful understanding are scrutinised. Questions and problems to solve are formulated to promote the processes associated with the solving of polynomial equations, and the solving procedures used by a group of college students are analysed. A teaching model/method, which targets the cognitive and affective domains, is presented. / Mathematics Education / M.A. (Mathematics Education)